Method for transforming a distortion-corrected magnetic resonance image, method for carrying out magnetic resonance measurements, and image transformation unit

ABSTRACT

A method for carrying out magnetic resonance measurements on an examination object in a magnetic resonance system is described. In at least one embodiment, a magnetic resonance image of the examination object previously acquired via the magnetic resonance system is used to determine spatial coordinates in order to control the magnetic resonance system for the magnetic resonance measurement to be carried out. In this case, in order to determine the spatial coordinates, use is made of a distortion-corrected magnetic resonance image generated on the basis of an original magnetic resonance measured image acquired by the magnetic resonance system and transformed in advance into an equivalent measured image on the basis of field inhomogeneity values of the magnetic resonance system. Also described are a method for, in at least one embodiment, transforming a distortion-corrected magnetic resonance image, generated on the basis of an original magnetic resonance measured image acquired by a magnetic resonance system into an equivalent measured image, and a suitable image transformation unit.

PRIORITY STATEMENT

This application is a divisional of application Ser. No. 11/826,587filed Jul. 17, 2007 which claims priority under 35 U.S.C. §119 on Germanpatent application number DE 10 2006 033 248.2 filed Jul. 18, 2006, theentire contents each of which are hereby incorporated herein byreference.

FIELD

Embodiments of the invention generally relate to a method for carryingout magnetic resonance images on an examination object in a magneticresonance system. For example, they may relate to one in the case ofwhich a magnetic resonance image of the examination object previouslyacquired by way of the magnetic resonance system is used to determinespatial coordinates in order to control the magnetic resonance systemfor the magnetic resonance measurement to be carried out. Furthermore,embodiments of the invention generally relate to a method, such as onewhich can be used for this purpose, for example. The method may relateto one for transforming a distortion-corrected magnetic resonance image,generated on the basis of an original magnetic resonance measured imageacquired by a magnetic resonance system into an equivalent measuredimage, which substantially matches the original magnetic resonancemeasured image. Furthermore embodiments of the invention generallyrelate to an image transformation unit, such as one for transforming adistortion-corrected magnetic resonance image acquired by a magneticresonance system and generated on the basis of an original magneticresonance measured image into an equivalent measured image, and/or to amagnetic resonance image with such an image transformation unit.

BACKGROUND

Magnetic resonance tomography, also termed nuclear magnetic resonancetomography, involves the technique, which has become wide spread in theinterim, for obtaining images of the body interior of a, usually living,examination object. In order to obtain an image with the aid of thismethod, it is firstly necessary to expose the body or the body part ofthe patient or test subject that is to be examined to a static basicmagnetic field that is generated by a basic field magnet of the magneticresonance system. During the acquisition of the magnetic resonanceimages, rapidly switched gradient fields that are generated by so calledgradient coils are superposed on this basic magnetic field for thepurpose of location coding.

Moreover, radiofrequency antennas are used to irradiate radiofrequencypulses of a defined field strength into the examination object. Thenuclear spins of the atoms in the examination object are excited by wayof these radiofrequency pulses in such a way that they are deflectedfrom their equilibrium position parallel to the basic magnetic field bya so called “excitation flip angle”. The nuclear spins then precessabout the direction of the basic magnetic field.

The magnetic resonance signals generated thereby are picked up byradiofrequency receiving antennas. Finally, the magnetic resonanceimages of the examination object are prepared on the basis of thereceived magnetic resonance signals. Each image pixel in the magneticresonance image is in this case assigned to a small body volume, a socalled “voxel”, and each brightness or intensity value of the imagepixels is combined with the signal amplitude, received from this voxel,of the magnetic resonance signal.

It is clear that there is a need for the presence of the mosthomogeneous fields possible in this method in order to obtain suitableimages. Thus, for example, field inhomogeneities of the gradientmagnetic fields mean that an object is shown in a two-dimensionalsectional image in a distorted fashion. If the inhomogeneities of thegradient magnetic field are known, a specific algorithm can be used tocarry out a distortion correction in order to generate from such anoriginal measured image a distortion-corrected image that correctlyreproduces the proportions of the object. The mathematical formulationof such a two-dimensional distortion and of the possible distortioncorrection is described, for example, in the article “Simulation of theInfluence of Magnetic Field Inhomogeneity and Distortion Correction inMR Imaging” by Ján Wei{hacek over (s)} and Lúbos Budinský in MagneticResonance Imaging, vol. 8, 1990.

In order, furthermore, to keep the inhomogeneities in the basic magneticfield as slight as possible when undertaking magnetic resonancemeasurement, a switch is being made more and more to using a so calledisocenter scanning method for measurement. In this case, all layers asnear as possible to the isocenter of the magnetic resonance unit or thebasic magnet are measured by appropriately displacing the table on whichthe patient or test subject lies during the measurement. The result ofthis is that large image fields such as, for example, the spinal columncannot be measured all at once. Such a measurement must then bedecomposed into a number of measuring steps, a measurement being carriedout station by station at the isocenter of the magnetic resonancemagnet. In order then to be able to reassemble the individual imagesgenerated in this case to form an overall image, it is necessary forthem to be subjected to two-dimensional distortion correction, somethingwhich can be performed in the known way.

In the routine operation, a very large portion of the patient is in themean time being examined using such an isocenter scanning method, theimages always being subjected to distortion correction as described. Inmost cases, however, a spectroscopy is then further arranged by a doctorresponsible after looking through the images. Thus, for example, in thecase of a so called “single voxel spectroscopy” a number of voxels areselected in a defined area in the sectional image of the patient/testsubject, and there is then generated for these a frequency spectrum withthe aid of which metabolites can be identified. The zone in which thisspectroscopy is to be carried out is defined as a rule in this casedirectly in the magnetic resonance images present with the aid of agraphics user surface.

If, for this purpose, the distortion-corrected images are used theproblem occurs the subsequent measurement may be carried out at thewrong location. This may be explained with the aid of FIG. 1. There, thefrequency f with which a specific location x is selected in the event ofthe emission of the corresponding radiofrequency pulses is plottedagainst the pertinent location x. In an ideal, that is to say completelyhomogeneous field, which corresponds to the ideal line depicted (dottedline), a real location x₀ in the examination object is also illustratedat the location x₀ in the image. This ideal behavior also indicates adistortion-corrected image. If the graphics user interface were now tobe used for the spectroscopy to select exactly this point x₀ in adistortion-corrected image, the measurement would however, operate withthe frequency f₂, since, after all, field inhomogeneities actually arepresent in reality. This would have the effect that finally, during thespectroscopy measurement the wrong location x₂ would be excited in theexamination object instead of the correct location x₀, since thefrequency f₂ corresponds to the location x₂ in accordance with therelationships actually present (continuous line). Thus, the distortedoriginal measured image is required in order to select the correctlocation for a subsequent spectroscopy measurement.

In this original measured image, a location x₀ is assigned a frequencyf₀ that is then displayed at the point x₁ in the distortion-correctedimage. It is then possible to select in this image the anatomy of thelocation x₀ at the pixel x₁ which contains the information relating tothe location x₀. The measurement is duly carried out thereupon with thefrequency f₀ such that measurement is performed correspondingly in theexamination object at the location x₀. That is to say, when selecting isspecific anatomy at the pixel x₁ in the distorted original measuredimage this is then also actually measured even if this anatomy lies atthe location x₀ in the real examination object.

This gives rise to the problem that, on the one hand,distortion-corrected images are required in order actually to be able toassemble images in an isocenter scanning method and, on the other hand,undistorted images are needed in order to be able to plan and correctlycontrol subsequent measurements. It is certainly true that it would bepossible for each magnetic resonance measurement with the aid of anisocenter scanning method also to store the distorted original images inthe database in addition to the distortion-corrected images.

However, this is not expedient, since then the data volume to be storedis unnecessarily increased. It is to be taken into account here that,after all, only a very small portion of the images initially generatedare actually used for later precise planning and control of a subsequentmeasurement. Since, consequently, virtually twice as many images thanare actually required must be handled in the image calculation,transferred and input into the database, this necessarily results in thefact that the performance of each image calculation is worsened.

This leads overall to the fact that the examination time per patient islengthened and the patient throughput is reduced. In addition, it can bethat a few examination sequences can no longer be carried out at all,such as, for example, spectroscopies with contrast agents, since theperiod for preparing the first images and the further planning anddetermination of the location for the subsequent spectroscopymeasurements lasts so long that the contrast agent is already washedout.

As an alternative it would be possible to repeat a part of themeasurement before planning a spectroscopy, in order to obtain therequired localization images not corrected for distortion. However, thisis likewise not acceptable, since this, too, also leads to a substantialtime loss and is attended by additional burdens for the patient. Here,as well, it can happen in the case of a contrast agent measurement thatthe actual spectroscopy measurement is no longer possible since thecontrast agent has already been washed out, as conditioned by the timeloss for the measurement of the additional images for planning thisspectroscopy.

The outcome of this set of problems in reality was that it has so farnot actually been possible to apply any isocenter scanning methods whenthere is a subsequent spectroscopy measurement to be carried outcorrectly.

SUMMARY

In at least one embodiment, the present invention specifies appropriatemethods and devices with the aid of which at least one of theabove-named set of problems is reduced or even circumvented.

In the case of the measuring method according to at least one embodimentof the invention, the spatial coordinates are determined simply on thebasis of a distortion-corrected magnetic resonance image generated onthe basis of an original magnetic resonance measured image acquired bythe magnetic resonance system, the magnetic resonance image being,however, back transformed into an “equivalent measured image” on thebasis of the field inhomogeneity values of the magnetic resonancesystem. That is to say, the problem is finally solved in the way thatthe original measured images are certainly corrected for distortion andare stored as previously in the isocenter scanning method asdistortion-corrected magnetic resonance images. However, after such adistortion-corrected magnetic resonance image has been selected in orderto carry out therein the plans for subsequent measurements, for examplein order to determine the spatial coordinates for a subsequentspectroscopy measurement, the magnetic image is then again backtransformed in advance into an equivalent measured image thatsubstantially corresponds to the original magnetic resonance measuredimage. Such a back transformation can be carried out substantially morequickly than a new measurement of a measured image in the required areathat has not been corrected for distortion. It is likewise not necessaryin the method to archive all the original measured images in addition tothe distortion-corrected magnetic resonance images. The entire methodcan therefore be carried out quickly and, above all, also costeffectively and with less of a burden for the patient.

A particularly suitable inventive transformation method of at least oneembodiment, for transforming such a distortion-corrected magneticresonance image into an equivalent measured image, is disclosed indetail below. In this case, the following method steps are respectivelycarried out for the individual pixels defined in an image raster of thedistortion-corrected magnetic resonance image:

It is firstly necessary to determine the field inhomogeneity values ofthe magnetic resonance system at the location of the relevant pixel.Such field inhomogeneity values of the magnetic resonance system areusually known, that is to say they are calculated or measured before ameasurement and stored in a database since they are required in any casefor the distortion correction itself. The determination of the fieldinhomogeneity values can therefore be performed by accessing therelevant memory in which the field inhomogeneity values are stored.

A displacement of the relevant pixel is then calculated on the basis ofthe determined field inhomogeneity values. That is to say, it isdetermined to where a specific pixel would be displaced in a measuredslice of the examination object during measurement by the fieldinhomogeneity values actually occurring in the original measured image.Finally, this real displacement also corresponds to the displacementthat must take place in the back transformation from thedistortion-corrected image to the equivalent measured image.

Furthermore, a distorted area of the relevant pixel is then calculatedon the basis of the determined field inhomogeneity values. It isdetermined in this case how a pixel of the examination object would becompressed or expanded because of the field inhomogeneities in theoriginal measured image. This, as well, must in turn be taken intoaccount in a back transformation of the distortion-corrected magneticresonance image into the equivalent measured image.

Subsequently, an overlap of this displaced and distorted area of therelevant pixel with the areas of the pixels defined in an image rasterof the equivalent measured image is then calculated. It is then possiblefor the intensity value of the relevant pixel of thedistortion-corrected magnetic resonance image to be split between thepixels of the equivalent measured image in accordance with thedetermined overlap.

If this method is now executed for each individual pixel of thedistortion-corrected magnetic resonance image, and the appropriateintensity values in the pixels are summed up in the image raster of theequivalent measured image, this yields the desired equivalent measuredimage, which corresponds substantially to the original measured image,apart from approximation errors, rounding errors etc. Thistransformation method is relatively fast and can therefore preferably beused in the course of the measuring method according to the invention.However, it is, moreover, also possible to conceive other uses of thetransformation method according to an embodiment of the invention.

In addition to an interface for acquiring a distortion-correctedmagnetic resonance image, this possibly being an interface with acustomary image reconstruction unit and/or an image memory, acorresponding image transformation unit requires a field inhomogeneitydetermination unit for determining field inhomogeneity values of themagnetic resonance system. It is also likewise possible here for this tobe an interface for accessing a corresponding data memory with thesevalues. Furthermore, there is a need for an image pixel calculating unitthat is appropriately designed such that it carries out the above-namedmethod steps of at least one embodiment for the individual pixelsdefined in an image raster of the distortion-corrected magneticresonance image, and distributes the intensity values between the pixelsof the equivalent measured image and sums them up. Moreover, the imagetransformation unit requires a suitable interface for outputting theequivalent measured image.

Such an image transformation unit is preferably integrated in a magneticresonance system, for example in a control terminal of the magneticresonance system at which the operator can also input the planning datafor the subsequent measurements at the same time. However, it is alsopossible in principle to implement such an image transformation unit inanother computer unit.

It is particularly preferred to implement the components required forthe image transformation unit, that is to say the interfaces, the fieldinhomogeneity determination unit and the pixel calculating unit, in theform of image software modules on a computer unit. By contrast with ahardware implementation, such a software implementation has theadvantage that even already existing magnetic resonance systems caneasily be retrofitted. The invention consequently comprises a computerprogram product that can be loaded directly into a memory of aprogrammable computer unit, for example in a control device of amagnetic resonance system, having program code segments, in order toexecute all the steps of the method according to at least one embodimentof the invention when the program is executed on the computer unit.

The dependent claims respectively contain particularly advantageousrefinements and developments of embodiments of the invention, it beingpossible, in particular, also to develop further the measuring methodaccording to embodiments of the invention in accordance with thedependent claims of the transformation method according to embodimentsof the invention. Likewise the image transformation unit according to atleast one embodiment of the invention can be developed further inaccordance with the dependent claims of the measuring method and thetransformation method.

Since the area, distorted on the basis of the field inhomogeneityvalues, of a pixel of the distortion-corrected magnetic resonance imagecan appear relatively complicated, this is approximated for the imagetransformation in order to reduce the computational outlay, preferablyby an area having a simple geometric shape. What is meant by simplegeometric shape for this purpose are triangles, rectangles, circles,polygons or other geometric shapes with a known area given specificdimensions.

The distorted area of a pixel of the distortion-corrected magneticresonance image is approximated with particular preference by anoctagonal or rectangular area. As is further shown later on, an octagonor a rectangle are areas in the case of which the dimensions of thedistorted or the approximated distorted area of a pixel can bedetermined in a particularly simple way on the basis ofdirection-dependent Jacobi factors that respectively represent a localfield gradient at the location of the relevant pixel. Thelocation-dependent and direction-dependent Jacobi factors are usuallydetermined and stored in any case in advance for a specific measurementor a magnetic resonance unit, in order to use these for the distortioncorrection, as well.

In order to distribute the intensity values of the relevant pixel of thedistortion-corrected magnetic resonance image between the pixels of theequivalent measured image in accordance with the determined overlap in asimple way, it is particularly preferred respectively to determine forthe relevant pixel weighting factors that respectively represent theoverlap of the distorted or approximated distorted area of the relevantdisplaced pixel with an area of a pixel of the equivalent measuredimage. The splitting of intensity value of the relevant displaced pixelof the distortion-corrected magnetic resonance image between the pixelsof the equivalent measured image then is performed in a fashionproportional to the determined weighting factors.

At least for a few pixels of the equivalent measured image, specificallythe edge pixels that overlap only partially with the displaced anddistorted or approximated distorted area, it is possible here for theweighting factors to be determined as a function of a distance of therespective midpoint of the relevant pixel of the equivalent measuredimage from the centroid of the displaced and distorted or approximateddistorted area of the relevant pixel.

Furthermore, the weighting factors are preferably determined as afunction of the number of the pixels of the equivalent measured imagewith the aid of which the distorted or approximated distorted surface atleast partially overlaps.

It has proved to be advantageous for a particularly simple and rapidcalculation when inhomogeneity intervals are defined, in a specificdirection of the image raster, as a function of a distance of thecentroid of the distorted or approximated distorted area of the relevantpixel of the distortion-corrected image from the midpoint of the nearestpixel of the equivalent measured image. These inhomogeneity intervalsare then respectively assigned specific weighting factors for theindividual pixels of the equivalent measured image as a function of thedistance of the midpoint of the distorted or approximated distorted areafrom the midpoint of the nearest pixel. It may then only be tested as towhether the direction-dependent Jacobi factor present at the relevantpixel of the distortion-corrected magnetic resonance image lies in aspecific intensity interval. If this is the case, the intensityfractions are correspondingly assigned to the relevant pixels of theequivalent measured image, which overlap with the distorted orapproximated distorted area, in accordance with the weighting factorsthat are assigned to this intensity interval.

As mentioned, in this case the weighting factors are also a function ofthe distance of the midpoint of the distorted or approximated distortedarea from the midpoint of the nearest pixel. That is to say, what isinvolved here in the actual sense is a weighting function that dependson this distance. This calculation can preferably be performedseparately in any direction of the image raster (column direction androw direction), and there are then formed, for example by multiplyingthe direction dependent weighting factors thus determined for eachpixel, overall weighting factors with the aid of which the fraction ofthe intensity value of a pixel of the distortion-corrected image thatfalls to the individual pixels of the equivalent measured image can becalculated.

The intensity values are preferably normalized before the division as afunction of a Jacobi factor, for example are divided by the product ofthe location-dependent Jacobi factors present at the relevant pixel.

The abovedescribed transformation method according to at least oneembodiment of the invention can be carried out very particularly quicklyand simply. Nevertheless, the measuring method according to at least oneembodiment of the invention can also be carried out in principle byusing other transformation methods as long as it is ensured that theequivalent measured image corresponds sufficiently to the originalmeasured image for it thus to be possible to carry out a reliabledetermination of spatial coordinates.

As previously described, the measuring method according to at least oneembodiment of the invention is particularly suitable for using theequivalent measured image to obtain spatial coordinates for a subsequentspectroscopy measurement. That is to say, the method according to atleast one embodiment of the invention now permits images obtained withthe aid of an isocenter scanning method also to be used for subsequentspectroscopy measurements without having to accept the disadvantagesmentioned at the beginning. However, the method can also be used inprinciple for other subsequent measurements such as, for example,chemical shift imaging (CSI).

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is explained in more detail below once again withreference to the attached figures and with the aid of exampleembodiments. Here, the same components are provided with identicalreference symbols in the various figures. In the drawings:

FIG. 1 shows a diagram for explaining the problem of determining thelocation of specific voxels in the case of distortion-corrected images,

FIG. 2 shows an illustration of the distortion of two pixels that iscaused by the field inhomogeneities of the gradient magnetic field,

FIG. 3 shows an illustration of various possibilities of approximatingthe distorted area by way of standard geometric shapes,

FIG. 4 shows an illustration for explaining the basic principle of theimage transformation according to an embodiment of the invention,

FIG. 5 shows an illustration for explaining the distribution of theintensity fractions of a distorted and displaced pixel of thedistortion-corrected image between the pixels of the equivalent measuredimage in the one-dimensional case,

FIG. 6 shows an illustration of the effect of the strength of the fieldinhomogeneity on the number of the pixels to be taken into account inthe case of the area overlap,

FIG. 7 shows an original measured image of a magnetic resonancemeasurement of a structured phantom in comparison to adistortion-corrected image, determined therefrom, and an equivalentmeasured image back transformed from the distortion-corrected image, and

FIG. 8 shows an illustration of the principle of a magnetic resonancesystem having an image transformation unit according to an embodiment ofthe invention.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the presentinvention. As used herein, the singular forms “a”, “an”, and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“includes” and/or “including”, when used in this specification, specifythe presence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Spatially relative terms, such as “beneath”, “below”, “lower”, “above”,“upper”, and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, term such as “below” can encompass both anorientation of above and below. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein are interpreted accordingly.

Although the terms first, second, etc. may be used herein to describevarious elements, components, regions, layers and/or sections, it shouldbe understood that these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are used onlyto distinguish one element, component, region, layer, or section fromanother region, layer, or section. Thus, a first element, component,region, layer, or section discussed below could be termed a secondelement, component, region, layer, or section without departing from theteachings of the present invention.

In describing example embodiments illustrated in the drawings, specificterminology is employed for the sake of clarity. However, the disclosureof this patent specification is not intended to be limited to thespecific terminology so selected and it is to be understood that eachspecific element includes all technical equivalents that operate in asimilar manner.

Referencing the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views, exampleembodiments of the present patent application are hereafter described.Like numbers refer to like elements throughout. As used herein, theterms “and/or” and “at least one of” include any and all combinations ofone or more of the associated listed items.

The set of problems that arises when positional data for a subsequentsingle voxel spectroscopy measurement are to be determined with the aidof a distortion-corrected image, and the magnetic resonance system is tobe driven using these data has already been explained at the beginningwith the aid of FIG. 1. The wrong frequency is then necessarily selectedowing to the distortion correction, and measurement is consequently madeat a wrong location. Images that are not distortion-corrected musttherefore be present for the determination of spatial coordinates inrelation to the subsequent measurement.

This is achieved in accordance with the invention by virtue of the factthat an “inverse distortion correction” is carried out with the aid ofthe images, and thus the distortion-corrected image is back transformedagain before the determination of the spatial coordinates on the basisof the field inhomogeneity values of the magnetic resonance system intoan equivalent measured image that corresponds substantially to theoriginal magnetic resonance measured image. It is then possible in thisequivalent measured image to plan the further measurements and determinespatial coordinates for the further measurements.

The basic principle of such an inverse distortion correction resides inthe fact that the pixels are displaced and distorted in the image rasterof the undistorted, distortion-corrected image in a way which alsohappens with the real voxels in the examination object in a specificsectional image plane when they are imaged in the original measuredimage by the magnetic resonance measurement. Reference may be made toFIG. 2 to this end. The left-hand side shows an image raster BR_(V) ofan undistorted, distortion-corrected image that consists of a number ofimage pixels P_(V) (only 4×4 pixels being illustrated here for the sakeof simplicity). These pixels P_(V) are displaced and stretched orcompressed by the field inhomogeneities, something which is caused bydistortion of the entire image raster BR_(V). This is shown on theright-hand side of FIG. 2, where the image raster BR_(V) of thedistortion-corrected image is illustrated in distorted form with dashedlines.

Superposed thereon with continuous lines is an image raster BR_(A) ofthe equivalent measured image that corresponds to the image raster ofthe actual original measured image, with the individual pixels P_(A).These images therefore also reflect how an object is illustrated in adistorted fashion without a distortion correction owing to the fieldinhomogeneities of the gradient coils. The distortion in the geometryand in the intensity at a specific location is a function in this caseof the local field gradient of the inhomogeneity.

The different effects on the individual image pixels illustrated in thiscase in FIG. 2 explicitly are two different image pixels P_(V1), P_(V2).The two of these are respectively displaced in a specific direction by aspecific displacement vector SH₁, SH₂. Moreover, the distortion has theeffect that one pixel P_(V1) is stretched in various directions andtherefore assumes a larger distorted area F_(V1). The second pixelP_(V2), by contrast, is compressed in various directions and thereforeassumes a smaller distorted area F_(V2). The original intensity of theindividual pixels is respectively distributed in this case over thedistorted area F_(V1), F_(V2) such that in addition to the geometricdistortion a change in intensity also occurs at the individual points.Finally, it is therefore necessary for the pixels not only to bedisplaced, but also to be adapted in their brightness with the aid of aspecific intensity interpolation as is further described below.

The local field gradient of the inhomogeneity at a specific pixel can beexpressed by means of the direction-dependent Jacobi factor. Arrangingthe Jacobi factors in a matrix in accordance with their direction rulederivative results in the so called Jacobi matrix, which characterizestransformation between the distorted and undistorted image.

A 2D distortion as in the present case is a projection in the form of:

$\begin{matrix}{\left. \begin{pmatrix}x \\y\end{pmatrix}\mapsto\begin{pmatrix}f_{x} \\f_{y}\end{pmatrix} \right. = {\begin{pmatrix}{x + {\Delta \; {{B\left( {x,y} \right)}/G_{x}}}} \\{y + {\Delta \; {{B\left( {x,y} \right)}/G_{y}}}}\end{pmatrix} = {\begin{pmatrix}x \\y\end{pmatrix} + {\begin{pmatrix}{\Delta \; {{B\left( {x,y} \right)}/G_{x}}} \\{\Delta \; {{B\left( {x,y} \right)}/G_{y}}}\end{pmatrix}.}}}} & (1)\end{matrix}$

Here, ΔB(x,y) is the gradient field inhomogeneity as a function of thelocation (x, y) which can be measured in advance once for the presentgradient field of the magnetic resonance system and/or be calculatedfrom the coil geometry. G_(j) in each case specifies the set desiredgradient at the relevant location in the direction j.

The entire term

$\begin{matrix}\begin{pmatrix}{\Delta \; {{B\left( {x,y} \right)}/G_{x}}} \\{\Delta \; {{B\left( {x,y} \right)}/G_{y}}}\end{pmatrix} & (2)\end{matrix}$

therefore constitutes the geometric displacement of an original pixel.When a slice to be measured has been selected by the user on themagnetic resonance unit, the spatial coordinates of all the voxels (orpixels within the selected image plane) are known. Since, moreover, asexplained above, the spatially dependent inhomogeneities ΔB(x,y) of thegradient coils are known it is also possible to calculate thedisplacement vector (SH₁, SH₂ in FIG. 2), that is to say the distancevector between distorted and undistorted pixels, for each pixel positionwith the aid of equation (2). A more detailed formula for calculatingthe distance vector is to be found, for example, in DE 10 2004 031 983.

The Jacobi matrix can then be defined as:

$\begin{matrix}{J = {\begin{pmatrix}J_{x} & J_{xy} \\J_{yx} & J_{y}\end{pmatrix} = {\begin{pmatrix}\frac{\partial f_{x}}{\partial x} & \frac{\partial f_{x}}{\partial y} \\\frac{\partial f_{y}}{\partial x} & \frac{\partial f_{y}}{\partial y}\end{pmatrix}.}}} & (3)\end{matrix}$

J_(x), J_(y), J_(xy), J_(yx) are the direction-dependent Jacobi factorshere.

The precise mathematical formulation of the 2D distortion is describedin the article by Ján Wei{hacek over (s)} and Lúbos Budinský alreadyindicated at the beginning.

As is easy to see from FIG. 2, a square pixel in an image plane of anobject is generally distorted by the field inhomogeneities onto an areathat cannot be described exactly by a simple geometric shape such as atriangle, a rectangle, a polygon or another geometric shape with asimple known area.

In order not to configure the back transformation method too intensivelywith regard to computation, the actually complicated area is thereforepreferably approximated by a simple geometric shape in the case of theinverse distortion correction. Possibilities for such an approximationare illustrated in FIG. 3, recourse being made to the example of thedistortion of the pixels P_(V1), P_(V2) in FIG. 2.

In the image at far left, the distorted areas F_(V1), F_(V2) areapproximated by simple rectangular areas FA_(V1), FA_(V2). Theapproximation is performed by lozenge-shaped areas FA′_(V1), FA′_(V2) inthe middle image, and by octagonal areas FA″_(V1), FA″_(V2) in the imageon the far right.

The extent of these areas in the various directions is a function inthis case of the direction dependent Jacobi factors. As is to be seen inFIG. 3 at right, an octagon can be described by way of the Jacobifactors on the main diagonals J_(x) and J_(y), and, furthermore, bymeans of the Jacobi factors J_(xy) and J_(yx) on the secondarydiagonals.

However, an example of a rectangular approximation shown on theleft-hand side in FIG. 3 constitutes the simplest case of such anapproximation. Such a simple approximation is assumed below, since it ispossible in this way to minimize the computing time for the inversedistortion correction. Only the Jacobi factors in the direction of thetwo main axes are then used for the edge length of the approximatedrectangular areas FA_(V1), FA_(V2) in the inverse distortion correction.J_(x) is the extent in the x-direction (row direction), and J_(y) theextent in the y-direction (column direction) of the image raster of theequivalent measured image, as is illustrated in the left-hand image inFIG. 3.

The fundamental mode of procedure for calculating the individual imagepixels of the equivalent measured image is explained with the aid ofFIG. 4. Illustrated again on the left-hand side is the image raster thatis shown on the left hand side in FIG. 3 and has the individual pixelsof the equivalent measured image and on which there is superposed thedistorted and displaced areas of the image pixels F_(V1), F_(V2) of theimage pixels P_(V1), P_(V2) of the distortion-corrected image. As hasbeen said, these areas are approximated with the aid of rectangularareas FA_(V1), FA_(V2) whose extent in the two directions isrespectively determined by the direction-dependent Jacobi factors J_(x),J_(y) at the location of the relevant pixel P_(V1), P_(V2) of thedistortion-corrected image.

Illustrated on the right-hand side of FIG. 4 is an enlarged part of thisimage raster that contains only the lower right hand area, 3×3 pixels insize, of the left-hand image in FIG. 4. It is illustrated hereschematically that the image intensity of the original pixels P_(V1),P_(V2) in the distortion-corrected measured image, which is nowdistributed between the approximated distorted areas FA_(V1), FA_(V2),relates not only to a single image pixel of the equivalent measuredimage, since, after all, the approximated distorted areas FA_(V1),FA_(V2) lie in a fashion offset from the image raster BR_(A) ofequivalent measured image. The image intensity of the individual pixelsis therefore distributed in accordance with the respective overlap ofthe approximated distorted area FA_(V1), FA_(V2) of the relevant imagepixels P_(V1), P_(V2) between the pixels P_(A11), P_(A12), P_(A13),P_(A21), P_(A22), P_(A23), P_(A31), P_(A32), P_(A33).

In the example illustrated in concrete terms, the intensity from thepixel P_(V1) originally present in the undistorted image raster BR_(V)of the distortion-corrected image is distributed between the threepixels in the upper row P_(A11), P_(A12), P_(A13) and in the middle rowP_(A12), P_(A21), P_(A23), since these pixels overlap with the distortedarea FA_(V1). Which intensity fraction is assigned to the individual newpixels P_(A11), P_(A12), P_(A13), P_(A21), P_(A22), P_(A23), is afunction of how large the overlap U₁₁, U₁₂, U₁₃, U₂₁, U₂₂, U₂₃ isbetween the rectangular area FA_(V1) and the relevant pixels P_(A11),P_(A12), P_(A13), P_(A21), P_(A22), P_(A23).

In the same way, the intensity of the second pixel P_(V2) in theundistorted image raster BR_(V) is distributed between the pixelsP_(A23), P_(A33) in the equivalent measured image, since the areaFA_(V2) overlaps with these two pixels P_(A23), P_(A33). It is clearthat in the case of the example illustrated in FIG. 4, the predominantportion of the intensity is assigned to the pixel P_(A23), and the pixelP_(A33) obtains only a very small fraction of the intensity value of theoriginal pixel P_(V2) because of the small overlap.

If a pixel of the distortion-corrected image were accidentally also onlyto fall into one pixel in the equivalent measured image, it is thenclear that the entire intensity is assigned to this pixel.

In accordance with the above explained basic idea, the following stepsare carried out for each individual pixel of the originaldistortion-corrected image within the image transformation method:

1. Firstly, the intensity value of the relevant pixel of thedistortion-corrected image is divided by the overall Jacobi factorJ=J_(x)·J_(y) present for this pixel. As a result, a prenormalization ofthe intensity values is carried out that compensates the changes inintensity, dependent on the Jacobi factor, that occur during the laterdistribution of the intensity values between the pixels of theequivalent measured image, such as are described in the subsequent thirdmethod step.

2. In a second step, knowledge of the field inhomogeneity is thenutilized to calculate where the midpoint or centroid of a pixel of thedistortion-corrected image is displaced to on the basis of the fieldinhomogeneities, that is to say the displacement vector (SH₁ and SH₂ inFIG. 2) is determined. This is performed with the aid of equation (2).

3. The distortion of the pixel is then determined on the basis of thefield inhomogeneities, and the original intensity of the pixel of thedistortion-corrected image is divided between the pixels of theequivalent measured image in accordance with the area overlap of theapproximated rectangular distorted area with the pixels in the gratingof the equivalent measured image.

The number of the pixels in the equivalent measured image between whichthe original intensity of the relevant pixel of the distortion-correctedimage is distributed is a function, as mentioned, of the Jacobi factors,that is to say the local field inhomogeneities at this point. Themaximum extent in the x- and y-directions is known on the basis ofknowledge of the image inhomogeneities, and so there is no need duringthe calculation to take account of more pixels for intensitydistribution than is mandatory. Reference may be made to FIGS. 5 and 6for this purpose.

FIG. 5 shows the calculation of the pixel intensity in the equivalentmeasured image with reference to an example in which the fieldinhomogeneity at the pixel P_(V) of the distortion-corrected imagecorresponds to a Jacobi factor of J_(x)=2. For the purpose ofsimplification, the Jacobi factor has been set here in the y-directionJ_(y)=1, that is to say no distortion takes place in this direction.Likewise, for the sake of simplicity it is only the case of a simpledisplacement SH in the x-direction that is illustrated here, since theexplanations can be substantially simplified with the aid of such a onedimensional case. However, the extension to the second dimension, thatis to say by a displacement of the y-direction with the aid of a Jacobifactor J_(y)≠1, can be performed in a primarily analogous fashion.

Illustrated on the left-hand side of FIG. 5 is an individual originalpixel P_(V) in the distortion-corrected image with the midpoint MP_(V).Illustrated schematically on the right-hand side is an image raster ofthe equivalent measured image that consists only of a row of five pixelsP_(A0), P_(A0), P_(A2), P_(A3), P_(A4) here, for the sake of simplicity.The pixel P_(V) of the distortion-corrected image is displaced in theimage raster BR_(A) of the equivalent measured image by the distance SHbetween the original position of the midpoint MP_(V) (here at 0.5 pixelwidths) and the centroid M_(V), which corresponds to the midpoint, ofthe distorted displaced area FA_(V) (here at approximately 2.1 pixelwidths). Here, the values relate to the scale depicted at the top inFIG. 5, in which the positions in the image raster are specified inpixel widths. If this displacement vector SH is known, it follows that,given a known midpoint MP_(V) of the pixel P_(V) in the raster BR_(V) ofthe distortion-corrected image, that it is also possible to determinethe centroid M_(V) of the approximated distorted area FA_(V) of theoriginal pixel P_(V), as well as the distance dx thereof from themidpoint M₀ of the nearest pixel P_(A0) of the equivalent measuredimage. The distances from the other pixel midpoints can likewise becalculated.

Since the Jacobi factor J_(x)=2 in the present example, the width of theoriginal pixel P_(V) is simply doubled. On the basis of this expansionand displacement SH, the pixel P_(V) now assumes in the image rasterBR_(A) of the equivalent measured image an area FA_(V) that overlaps themiddle image pixel P_(A0) in the image raster BR_(A) of the equivalentmeasured image completely, and still partially overlaps the neighboringimage pixels P_(A1), P_(A2). The numeration of the pixels P_(A0),P_(A1), P_(A2), P_(A3), P_(A4) is arbitrary in principle, but isperformed here for the sake of simplicity in accordance with thedistance of the respective midpoints of the individual pixels from themidpoint or centroid M_(V) of the approximated distorted area FA_(V) ofthe original pixel P_(V), since this notation is also used in theformulas still to follow.

It is also immediately to be seen from FIG. 5 that the number of theoverlapped pixels in the equivalent measured image is a function of theJacobi factor J. Given a Jacobi factor J_(x)=2, the distorted areaFA_(V) assumes the length of precisely two pixels in the x-direction.Consequently, at least two neighboring pixels are overlapped by thisarea, but at most three neighboring pixels can be overlapped.Furthermore, it is also to be seen that the number of the overlappedpixels is also a function of the geometric displacement of the pixel,specifically finally of the distance dx between the midpoint M_(V) ofthe displaced and distorted area FA_(V) of the original pixel P_(V) andthe midpoint M₀ of the nearest pixel P_(A0).

This is explained once again with the aid of FIG. 6, in which theoriginal pixel P_(V) is illustrated again on the left-hand side (but nowsomewhat narrower for reasons of space in the y-direction), and thedisplaced and distorted area inside the image raster BR_(A) of theequivalent measured image is illustrated on the right-hand side. Thedisplacement vector again respectively corresponds in this case to thedisplacement vector in FIG. 5. Consequently, the distance dx between themidpoint M_(V) of the displaced area FA_(V) and the nearest pixel P_(A0)corresponds to the value of FIG. 5.

However, another Jacobi factor J_(x) is selected in each row. In thefirst row, the Jacobi factor J_(x) corresponds to the value 1-2·dx(units again in pixel width), in the second row it corresponds to thevalue 1+2·dx, a third row to the value 3−2·dx, and in the fourth row tothe value 3+2·dx. Consequently, only one pixel is affected in the firstrow, that is to say the distorted area lies wholly in the middle pixel.In the second row, two neighboring pixels are affected, threeneighboring pixels are affected in the third row, and a total of fourneighboring pixels are affected in the fourth row, a new pixel alwaysbeing added alternatively right and left next to the nearest pixelP_(A0).

It is also possible to illustrate with the aid of FIGS. 5 and 6 that theoverlap of the displaced and distorted area FA_(V) of the original pixelP_(V) with the pixels P_(A1), P_(A2), acquired only from the edge of thearea FA_(V), in the image raster BR_(A) of the equivalent measured imageis a function of the distance dx between the midpoint M_(V) of the areaFA_(V) and the nearest pixel P_(A0). The nearest pixel P_(A0) has anoverlap area U₀ that corresponds to the entire pixel, that is to saythis pixel is wholly overlapped. However, of the first pixel P_(A1)lying alongside on the left only an area U₃ is affected whose lengthcorresponds in the direction of the raster row to 0.5+dx (units in pixelwidth). The length of the overlap area U₂ of the pixel P_(A2) lying onthe right next to the middle pixel P_(A0) corresponds, by contrast, onlyto the value 0.5−dx.

It is thus possible to define specific inhomogeneity intervals for whichit is possible to determine weighting factors W by which it is necessaryonly to multiply the original intensity of the original pixel P_(V) inthe distortion-corrected image in order to obtain the intensity valuethat can be assigned to the individual pixels P_(A0), P_(A1), P_(A2),P_(A3), P_(A4) in the equivalent measured image on the basis of thispixel.

The following relationships apply in this case to the example of therectangular model shown in FIG. 5:

Inhomogeneity Affected interval Weighting factor pixels 0 < |J_(x)| ≦ 1− 2 · dx W_(x)[0] = |J_(x)| 1 1 − 2 · dx < |J_(x)| ≦ 1 + 2 · dx W_(x)[0]= 0.5 · (|J_(x)| + 1) − dx 2 W_(x)[1] = 0.5 · (|J_(x)| − 1) + dx 1 + 2 ·dx < |J_(x)| ≦ 3 − 2 · dx W_(x)[0] = 1 3 W_(x)[1] = 0.5 · (|J_(x)|− 1) + dx W_(x)[2] = 0.5 · (|J_(x)| − 1) − dx 3 − 2 · dx < |J_(x)| ≦ 3 +2 · dx W_(x)[0] = 1 4 W_(x)[1] = 0.5 · (|J_(x)| − 1) + dx W_(x)[2] = 0.5· (|J_(x)| − 1) − dx 3 + 2 · dx < |J_(x)| ≦ 5 − 2 · dx W_(x)[0] =W_(x)[1] = W_(x)[2] = 1 5 W_(x)[3] = 0.5 · (|J_(x)| − 3) + dx W_(x)[4] =0.5 · (|J_(x)| − 3) − dx . . . . . . . . .W_(x) [i] in this case denotes the weighting factor in the x-directionfor the pixel i, the numeration i=0, 1, 2, 3, 4 . . . having beenselected in accordance with the distance of the relevant pixel from themidpoint of the displaced area FA_(V) of the pixel P_(V) (compare FIG.5). However, this numeration is fundamentally arbitrary. The last columnindicates the number of the pixels, for which the distorted areaextends.

In these equations, the parameter d_(x) likewise again denotes thedistance between the midpoint A_(V) of the displaced area FA_(V) and themidpoint M₀ of the nearest pixel PA_(V) (compare FIG. 5). The valuerange can in this case be between 0 and at most half the pixel length.

It is also possible in principle to describe the above-namedrelationship by means of a general recursive formula (with kε{1,3,5,7,9,. . . }):

Inhomogeneity Affected interval Weighting factor pixels 0 < |J_(x)| ≦ 1− 2 · dx W_(x)[0] = |J_(x)| 1 k − 2 · dx < |J_(x)| ≦ k + 2 · dx W_(x)[0]= . . . = W_(x)[k − 2] = 1 (if k > 1) k + 1 W_(x)[k − 1] = 0.5 ·(|J_(x)| − (k − 2)) − dx W_(x)[k] = 0.5 · (|J_(x)| − k)) + dx k + 2 · dx< |J_(x)| ≦ (k + 2) − 2 · dx W_(x)[0] = . . . = W_(x)[k − 1] = 1 (ifk > 1) k + 2 W_(x)[k − 1] = 0.5 · (|J_(x)| − k) + dx W_(x)[k] = 0.5 ·(|J_(x)| − k) − dx.

The above equations can be explained once again using the followingexample:

If the Jacobi factor J_(x) of a distortion-corrected pixel lies in therange of

1−2·dx<|J _(x)|≦1+2·dx,  (4a)

the original intensity of the distortion-corrected pixel is thenmultiplied by

W _(x)[0]=0.5·(|J _(x)|+1)−dx  (4b)

and allocated to the pixel of the equivalent measured image whosemidpoint lies closest to the centroid of the displaced and distortedpixel of the distortion-corrected image. The next pixel but one (that isto say the pixel in the equivalent measured image having the secondsmallest distance from the centroid of the displaced and distorted pixelof the distortion-corrected image) has the intensity fraction

W _(x)[1]=0.5·(|J _(x)|−1)+dx  (4c)

of the original intensity.

In this way, the distortion-corrected image is run through pixel bypixel, and the original intensities are distributed between the pixelsof the equivalent measured image and summed up. The principle applies inan entirely analogous fashion to the y-direction. That is to say, it ispossible to calculate an overall weighting factor W per individual pixelthat is the product of the individual weighting factors W_(x) and W_(y),it being possible to calculate the individual weighting factors W_(x)and W_(y) using the abovedescribed system of equations within specificinhomogeneity intervals.

Since the sum of the weighting factors per pixel corresponds to theproduct |J_(x)|·|J_(y)| of the absolute values of the Jacobi factorsJ_(x) and J_(y), the prenormalization described in the first step mustbe carried out so that the overall weight finally corresponds to 1.

During the calculation, the abovedescribed recursive formula need,however, be implemented only as far as precisely the highestinhomogeneity occurring at all in the magnetic resonance system is beingconsidered. However, the formula can be appropriately expanded at anytime if it is to be applied for a magnetic resonance gradient systemthat then has a higher inhomogeneity. It can thereby be ensured that theoutlay on calculation takes up only the computing power that is requiredby the respective inhomogeneity. Possibly, no unnecessary weightingfactors are calculated which would only be equal to 0. This can beillustrated by the following example:

Assumption of concrete values of x=0.1 m, for G_(x)=10 mT/m=0.01 T/m andΔB(x)=x²/10 yields the following:

$J_{x} = {{1 + \frac{x}{5G_{x}}} = {{1 + \frac{0.1}{5 \cdot 0.01}} = {{1 + 2} = 3}}}$and${{\Delta \; {B\left( {x = 0.1} \right)}} = {{\frac{(0.1)^{2}}{10}T} = {{0.001T} = {1m\; T}}}},$

(that is to say 1000 ppm given a basic field of 1T).

Where J_(x)=3 the highest inhomogeneity occurring in the system, a pixelwould be stretched at most to 3 pixels. The algorithm would then have totake account of at most a stretching of 4 pixels since, for an arbitraryposition of the centroid of the distorted area, an expansion over 3pixel lengths can never extend beyond more than 4 pixels.

FIG. 7 shows first results of magnetic resonance experiments on aspecific phantom with a specific point pattern. Reproduced at top leftin FIG. 7 is the original measured image, which is obtained during amagnetic resonance measurement without a two dimensional distortioncorrection. A two-dimensional distortion correction produces therefromthe distortion-corrected image that is illustrated at top right. Thisimage finally reproduces the structure of the phantom exactly, that isto say without distortion.

The image at bottom left shows the equivalent measured image B_(A)generated from the distortion-corrected image B_(V) with the aid of themethod precisely described above. It is to be seen here straightawaythat the original measured image of the equivalent measured imagecorrespond very well. The above-described approximative method for backtransformation, which can be carried out exceptionally quickly, istherefore well suited for generating from the distortion-correctedimages equivalent measured images that correspond to the originalmeasured images except for slight inaccuracies.

A magnetic resonance system that can be used to carry out an embodimentof the invention is explained below with the aid of FIG. 8.

What is involved here is a magnetic resonance system that is customaryper se but in which the system control device 5 has been modified in asuitable way such that the magnetic resonance system 1 has an inventiveimage transformation unit 15 for carrying out the method according to anembodiment of the invention.

An essential item of this magnetic resonance system 1 is a recordingdevice 2, also termed “tomograph” or “scanner”, in which a patient 0 ispositioned on a couch 4 in an annular basic field magnet 3. Locatedinside the basic field magnet 3 is a radiofrequency antenna (notillustrated) for emitting the magnetic resonance radiofrequency pulses.Moreover, suitable gradient coils (likewise not illustrated) are locatedin the tomograph 2 in order to set the requisite magnetic fieldgradients. The tomograph 2 is driven by a system control device 5 thatis illustrated separately here. Connected to the system control device 5via an interface 9 is a terminal 20 that serves as user interface viawhich an operator operates the system control device 5, and thus thetomograph 2. The system control device 5 further comprises a bulkstorage 8 that serves to store images recorded, for example, by way ofthe magnetic resonance system 1.

The system control device 5 further has a tomograph interface 6 that isconnected to the tomograph 2 and, in accordance with the measurementrecord prescribed by way of the system control device 5, outputs theradiofrequency pulses with the suitable amplitudes and phases, as wellas the matching gradient pulses to the matching components of thetomograph 2 in order to carry out a specific measurement. Themeasurement sequences are controlled on the basis of the prescribedmeasurement records in this case by using a measurement sequence controlunit 12. The operator can communicate with this measurement sequencecontrol unit 12 with the aid of the terminal 22 and thus call upspecific measurement records and, if appropriate, modify them or elseprescribe new measurement records.

Furthermore, the system control device 5 is connected to the tomograph 2via an acquisition interface 7. The acquisition interface 7 is used toacquire the raw data RD that come from the tomograph 2 and arereconstructed in an image reconstruction unit 13 to form the desiredmagnetic resonance images.

These magnetic resonance images are then corrected for distortion in adistortion correction unit 14 (which, however, can also already be acomponent of the image reconstruction unit 13). The distortion-correctedmagnetic resonance images B_(V) can then be displayed via the interface9 on the terminal 20 individually or also in a fashion assembled by anisocenter scanning method, and/or be stored in the memory 8.

In particular, the images B_(V) can also be used in principle on theterminal 20 to carry out planning for further measurements, doing so byusing a mouse 21 or another pointing device of a graphics user interfaceto mark specific areas in the images at which further measurements, forexample single voxel spectroscopy, are then carried out. In this case,spatial coordinates x₀, at which the spectroscopy is to be carried out,generated with the aid of the user interface are then sent to themeasurement sequence control unit 12 such that the measurement sequencesfor the measurements to be carried out are appropriately generatedthere. In order to be able to determine the spatial coordinates x₀correctly, it is, however, necessary—as already described at thebeginning—to have available images that are not corrected fordistortion.

To this end, the system control unit 5 has an image transformation unit15. This image transformation unit 15 can call up distortion-correctedimages B_(V) from the memory 8 by means of an interface 16. Moreover,this image transformation unit 15 has a field inhomogeneitydetermination unit. What is involved here is a further interface 17 withthe aid of which the inhomogeneity values IW of the system 1 that arestored in a database in the memory 8 can be called up. With the aid ofthese determined inhomogeneity values IW, the abovedescribedcalculations for the individual image pixels of the distortion-correctedimage B_(V) are carried out inside an image pixel calculating unit 18,and an equivalent measured image B_(A) is thus generated. The latter canbe output in turn via the interface 19 of the image transformation unit15 and, for example, be stored in the memory 8, or be displayed directlyon the screen of the terminal 20 via the interface 9 such that it ispossible then to use this equivalent measured image B_(A) to determinethe correct spatial coordinates x₀ for the subsequent measurements.

The measurement sequence control unit 12, the image reconstruction unit13, the distortion correction unit 14 and the complete imagetransformation unit 15 together with all the interfaces 16, 17, 19 andthe image pixel calculating unit 18 can be implemented in the form ofsuitable software components, as here on a microprocessor 10, oralternatively of a number of networked microprocessors, of the systemcontrol device 5.

Both the system control device 5 and the terminal 20 and the memory 8can also be an integral component of the tomograph 2. However, it islikewise also possible for the system control device 5 to comprise anumber of individual components. In particular, for example, the massstorage 8 can, like the terminal 21, be connected via an interface tothe system control device 5, instead of being integrated therein.

Moreover, the entire magnetic resonance system 1 also has all thefurther usual components and features such as, for example, interfacesfor connection to a communications network, for example an imageinformation system. All these components that are not necessary forunderstanding embodiments of the invention are, however, not illustratedin FIG. 1 for reasons of better clarity.

It is likewise also possible for the image transformation unit to beimplemented on another computer unit, for example connected to thesystem control unit 5 via a bus system, there being connected in turn tosaid computer unit a suitable terminal via which an operator, forexample a doctor, can view images and carry out appropriate planningand/or define spatial coordinates for further measurements.

It may be pointed out once more in conclusion that the method describedabove in detail and the magnetic resonance system illustrated are merelyexample embodiments that can be modified by the person skilled in theart in multifarious ways without departing from the scope of theinvention. Embodiments of the invention have been explainedpredominantly with the aid of its use in a magnetic resonance systememployed in medicine. However, it is not limited to such use, but canalso be employed in scientific and/or industrial uses.

Further, elements and/or features of different example embodiments maybe combined with each other and/or substituted for each other within thescope of this disclosure and appended claims.

Still further, any one of the above-described and other example featuresof the present invention may be embodied in the form of an apparatus,method, system, computer program and computer program product. Forexample, of the aforementioned methods may be embodied in the form of asystem or device, including, but not limited to, any of the structurefor performing the methodology illustrated in the drawings.

Even further, any of the aforementioned methods may be embodied in theform of a program. The program may be stored on a computer readablemedia and is adapted to perform any one of the aforementioned methodswhen run on a computer device (a device including a processor). Thus,the storage medium or computer readable medium, is adapted to storeinformation and is adapted to interact with a data processing facilityor computer device to perform the method of any of the above mentionedembodiments.

The storage medium may be a built-in medium installed inside a computerdevice main body or a removable medium arranged so that it can beseparated from the computer device main body. Examples of the built-inmedium include, but are not limited to, rewriteable non-volatilememories, such as ROMs and flash memories, and hard disks. Examples ofthe removable medium include, but are not limited to, optical storagemedia such as CD-ROMs and DVDs; magneto-optical storage media, such asMOs; magnetism storage media, including but not limited to floppy disks(trademark), cassette tapes, and removable hard disks; media with abuilt-in rewriteable non-volatile memory, including but not limited tomemory cards; and media with a built-in ROM, including but not limitedto ROM cassettes; etc. Furthermore, various information regarding storedimages, for example, property information, may be stored in any otherform, or it may be provided in other ways.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the present invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the following claims.

1. A method for transforming a distortion-corrected magnetic resonanceimage, generated on the basis of an original magnetic resonance measuredimage acquired by a magnetic resonance system into an equivalentmeasured image, the method, carried out for individual pixels defined inan image raster of the distortion-corrected magnetic resonance image,comprising: determining field inhomogeneity values of the magneticresonance system at a location of a relevant pixel; calculatingdisplacement of the relevant pixel on the basis of the determined fieldinhomogeneity values; determining a distorted area of the relevant pixelon the basis of the determined field inhomogeneity values; determiningan overlap of the determined distorted area of the relevant pixel withareas of pixels defined in an image raster of the equivalent measuredimage; and splitting an intensity value of the relevant pixel of thedistortion-corrected magnetic resonance image between the pixels of theequivalent measured image in accordance with the determined overlap. 2.The method as claimed in claim 1, wherein the distorted area of a pixelof the distortion-corrected magnetic resonance image is approximated byan area (with a simple geometric shape.
 3. The method as claimed inclaim 2, wherein the distorted area of a pixel of thedistortion-corrected magnetic resonance image is approximated by atleast one of a rectangular and octagonal area.
 4. The method as claimedin claim 1, wherein the dimensions of the distorted area of a pixel ofthe distortion-corrected magnetic resonance image are determined on thebasis of direction dependent Jacobi factors that respectively representa local field gradient at the location of the relevant pixel.
 5. Themethod as claimed in claim 1, wherein weighting factors are determinedfor the relevant pixel that respectively represent an overlap of thedistorted area of the relevant displaced pixel with an area of a pixelof the equivalent measured image, and the splitting of intensity valueof the relevant displaced pixel of the distortion-corrected magneticresonance image between the pixels of the equivalent measured image isperformed in a fashion proportional to the determined weighting factors.6. The method as claimed in claim 5, wherein, at least for some of thepixels of the equivalent measured image, the weighting factors aredetermined as a function of a distance of the respective midpoint of therelevant pixel of the equivalent measured image from the midpoint of thedisplaced and distorted area.
 7. The method as claimed in claim 6,wherein the weighting factors are determined as a function of the numberof the pixels of the equivalent measured image with the aid of which thedistorted surface at least partially overlaps.
 8. The method as claimedin claim 7, wherein there are defined in a specific direction, as afunction of a distance of the centroid of the distorted area from themidpoint of the nearest pixel of the equivalent measured image,inhomogeneity intervals that are respectively assigned specificweighting factors for the individual pixels of equivalent measured imageas a function of the distance of the centroid of the distorted area fromthe midpoint of the nearest pixel, and the intensity fractions of therelevant pixels of the equivalent measured image are assigned as afunction of a specific one of these weighting factors when the directiondependent Jacobi factor present for the relevant pixel of thedistortion-corrected image lies in the pertinent intensity interval. 9.The method as claimed in claim 1, wherein the intensity value of therelevant pixel of the distortion-corrected magnetic resonance image isnormalized as a function of a Jacobi factor.
 10. A method for carryingout at least one magnetic resonance measurement on an examination objectin a magnetic resonance system, the method comprising: using a magneticresonance image of the examination object, previously acquired via themagnetic resonance system, to determine spatial coordinates in order tocontrol the magnetic resonance system for the at least one magneticresonance measurement to be carried out, wherein, to determine thespatial coordinates, a distortion-corrected magnetic resonance image isused, acquired by the magnetic resonance system, generated on the basisof an original magnetic resonance measured image and transformed inadvance into an equivalent measured image on the basis of fieldinhomogeneity values of the magnetic resonance system, wherein thetransforming occurs via the method as claimed in claim
 1. 11. An imagetransformation unit for transforming into an equivalent measured imageof a distortion-corrected magnetic resonance image generated on thebasis of an original magnetic resonance measured image acquired by amagnetic resonance system, comprising: an interface to acquire adistortion-corrected magnetic resonance image; a field inhomogeneitydetermination unit to determine field inhomogeneity values of themagnetic resonance system; an image pixel calculating unit to carry outthe following for the individual pixels defined in an image raster ofthe distortion-corrected magnetic resonance image, calculating adisplacement of the relevant pixel on the basis of the determined fieldinhomogeneity values, determining a distorted area of the relevant pixelon the basis of the determined field inhomogeneity values; calculatingan overlap of the determined distorted area of the relevant pixel withareas of pixels defined in an image raster of the equivalent measuredimage, splitting an intensity value of the relevant pixel of thedistortion-corrected magnetic resonance image between the pixels of theequivalent measured image in accordance with the determined overlap, andan interface to output the equivalent measured image.
 12. A magneticresonance system comprising an image transformation unit as claimed inclaim
 11. 13. A computer program product, directly loadable into amemory of a programmable computer unit, including program code segmentsto execute the method as claimed in claim 1 when the program is executedon the computer unit.
 14. A method for a magnetic resonance system, themethod comprising: acquiring, via the magnetic resonance system, anoriginal magnetic resonance measured image of the examination object;transforming the acquired image into an equivalent measured image on thebasis of field inhomogeneity values of the magnetic resonance system;and determining spatial coordinates of the transformed image to controlthe magnetic resonance system.
 15. The method of claim 14, furthercomprising: carrying out at least one magnetic resonance measurement onthe magnetic resonance system based upon the determined spatialcoordinates.
 16. The method of claim 14, further comprising: controllingthe magnetic resonance system based upon the determined spatialcoordinates.
 17. A computer readable medium including program segmentsfor, when executed on a computer device, causing the computer device toimplement the method of claim
 14. 18. A computer readable mediumincluding program segments for, when executed on a computer device,causing the computer device to implement the method of claim 1.